Bradford have failed to get the result of Sunday's loss to Leeds overturned, but coach Steve McNamara will escape action for his comments.
McNamara escaped censure for his comments after Bradford's loss
The Bulls asked Leeds to hand over the points after referee Steve Ganson admitted wrongly awarding a try.
Jordan Tansey's controversial late score gave Leeds a 42-38 win.
"Our operational rules state a club is not entitled to object to a result on the grounds of a match official's decision," said an RFL spokesman.
Slow-motion replays indicated Tansey was offside as he chased captain Kevin Sinfield's penalty kick at goal which rebounded off a post.
Ganson admitted he ought to have consulted video referee Ashley Klein.
McNamara, the new Great Britain assistant coach, claimed in the post-match news conference that Ganson "invented the penalty" and that his side were cheated out of victory.
Bradford chairman Peter Hood made it clear that McNamara would have the full backing of his club had the League decided to press charges over his comments.
But a spokesman added: "Due to the unique set of circumstances we are not planning to take any action regarding Steve McNamara's after-match comments."
Meanwhile, Bradford hooker Terry Newton will face the League's disciplinary committee on Wednesday after being charged with striking.
The Great Britain international was put on report by Ganson in the 12th minute for an alleged high tackle on Leeds front-rower Jamie Thackray.
Newton served a two-match ban earlier this season after being found guilty of striking St Helens forward Jon Wilkin and a suspension of any kind would rule him out of Sunday's Challenge Cup fifth-round tie at Wakefield.